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Journal of High Energy Physics

, 2013:150

First Online: 19 November 2013Received: 30 October 2013Accepted: 01 November 2013 Abstract

A recent, integrability-based conjecture in the framework of the Wilson loop OPE for \ \mathcal{N}=4 \ SYM theory, predicts the leading OPE contribution for the hexagon MHV remainder function and NMHV ratio function to all loops, in integral form. We prove that these integrals evaluate to a particular basis of harmonic polylogarithms, at any order in the weak coupling expansion. The proof constitutes an algorithm for the direct computation of the integrals, which we employ in order to obtain the full NMHV OPE contribution in question up to 6 loops, and certain parts of it up to 12 loops. We attach computer-readable files with our results, as well as an algorithm implementation which may be readily used to generate higher-loop corrections. The feasibility of obtaining the explicit kinematical dependence of the first term in the OPE in principle at arbitrary loop order, offers promise for the suitability of this approach as a non-perturbative description of Wilson loops-scattering amplitudes.

KeywordsSupersymmetric gauge theory Wilson ’t Hooft and Polyakov loops Scattering Amplitudes AdS-CFT Correspondence ArXiv ePrint: 1310.5735

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Autor: Georgios Papathanasiou

Fuente: https://link.springer.com/

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